Radial Compensation: Fixing Radius Distortion in Chart-Based Generative Models on Riemannian Manifolds

ArXi:2511.14056v2 Announce Type: replace-cross We study the base distribution in chart-based generative models on Riemannian manifolds. Standard methods sample in Euclidean tangent space and then map the sample to the manifold with a chart. This is convenient, but it changes the meaning of distance: the same tangent-space scale can correspond to different geodesic radii, i.e. shortest-path distances from a reference point on the manifold, under different charts, curvatures, and dimensions.